Lifting heptagon symbols to functions

DOI10.1007/JHEP10(2020)031zbMATH Open1456.81428arXiv2007.12966MaRDI QIDQ2657725

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Publication date: 14 March 2021

Published in: (Search for Journal in Brave)

Abstract: Seven-point amplitudes in planar $calN=4$ super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster bootstrap, but only at the level of the symbol. We promote these symbols to actual functions, by specifying their first derivatives and boundary conditions on a particular two-dimensional surface. To do this, we impose branch-cut conditions and construct the entire heptagon function space through weight six. We plot the amplitudes on a few lines in the bulk Euclidean region, and explore the properties of the heptagon function space under the coaction associated with multiple polylogarithms.

Full work available at URL: https://arxiv.org/abs/2007.12966

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